Conclusion

Overall I’m happy with my models and analysis for the non-accelerating point charge. The Mathematica animations demonstrate that the equations describe their physical counterparts well, and the proportionality between the electric potential and time for different spacial assumptions was interesting to investigate. Ideally I would have been able to adequately represent the magnetic vector potential field in Mathematica as well.

With more time I’d also try to generate a better model for the circular motion case, whether that means finding a mistake in my derivation or using a different underlying assumption or driving equation. I’d be interested in investigating other particle trajectories as well, perhaps defining more intricate ones but imposing a time-domain restriction.

And of course, there’s always the electric and magnetic fields themselves. To derive the E and B fields for a few simple particle trajectories would be interesting and challenging, and might segway well into some of the material from Griffiths relativity chapter. On page 528 is an alternate derivation for equation 10.68, which is the electric field of a moving point charge. The chapter 12 derivation is described as being both more efficient and more intuitive, and I think it would be worthwhile to take the time to compare the two. Problem 10.15 presents another relativity topic I would have liked to reach: the event horizon. The concept of retarded time is closely linked to any explanation of time dilation or simultaneity, and I would try to unfold the problem with this in mind.